clients <- read.csv("customers.csv", header = TRUE)
produits <- read.csv("products.csv", header = TRUE)
transactions <- read.csv("transactions.csv", header = TRUE)
summary(clients)
## client_id sex birth
## Length:8623 Length:8623 Min. :1929
## Class :character Class :character 1st Qu.:1966
## Mode :character Mode :character Median :1979
## Mean :1978
## 3rd Qu.:1992
## Max. :2004
summary(produits)
## id_prod price categ
## Length:3287 Min. : -1.00 Min. :0.0000
## Class :character 1st Qu.: 6.99 1st Qu.:0.0000
## Mode :character Median : 13.06 Median :0.0000
## Mean : 21.86 Mean :0.3702
## 3rd Qu.: 22.99 3rd Qu.:1.0000
## Max. :300.00 Max. :2.0000
summary(transactions)
## id_prod date session_id client_id
## Length:679532 Length:679532 Length:679532 Length:679532
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
Nous observons qu’il y a au moins un prix négatif au sein du dataframe “produits”. Nous prendrons le parti de le(s) remplacer par la moyenne à savoir 21,86. Nous allons également transposer les catégories en facteurs.
produits$categ <- as.factor(produits$categ)
Commençons par créer une copie de “produits”, “clients” et “transactions :
prod <- produits
clients2 <- clients
trans <- transactions
Remplaçons maintenant les valeurs négatives par la moyenne :
prod$price[prod$price<=0] <- 21.86
Assurons nous qu’il n’y ait plus de prix négatif :
summary(prod)
## id_prod price categ
## Length:3287 Min. : 0.62 0:2309
## Class :character 1st Qu.: 6.99 1: 739
## Mode :character Median : 13.09 2: 239
## Mean : 21.86
## 3rd Qu.: 22.99
## Max. :300.00
Tout est ok ✓.
outlier_prod <- unique(prod$id_prod)
outlier_client <- unique(clients2$client_id)
En observant le dataframe “transactions”, nous nous apercevons de la présence de transactions test, toutes effectuées à la même date (2021-03-01) par des clients fictifs (ct_0 et ct_1) sur le même produit (T_0).
head(sort(outlier_prod, decreasing = TRUE))
## [1] "T_0" "2_99" "2_98" "2_97" "2_96" "2_95"
head(sort(outlier_client, decreasing = TRUE))
## [1] "ct_1" "ct_0" "c_999" "c_998" "c_997" "c_996"
Vérifions le prix du produit correspondant à l’id T_0 :
prod$price[prod$id_prod == "T_0"]
## [1] 21.86
Au vue de la structure de leurs id, il semblerait qu’il s’agisse de transactions tests réalisées probablement lors du lancement du site. Nous décidons donc de supprimer le produit, les clients ainsi que les transactions associées à ces derniers :
prod_t <- which(prod$id_prod == "T_0")
prod <- prod[-prod_t,]
clients_t0 <- which(clients2$client_id == "ct_0")
clients_t1 <- which(clients2$client_id == "ct_1")
clients2 <- clients2[-clients_t1,]
clients2 <- clients2[-clients_t0,]
trans_t <- which(trans$id_prod == "T_0")
trans <- trans[-trans_t,]
Tout a bien été supprimé ✓.
id_clients1 <- unique(clients2$client_id)
id_clients2 <- unique(trans$client_id)
id_clients3 <- intersect(id_clients1, id_clients2)
Nous avons un total de 21 clients inactifs au sein de notre base de données. Isolons les afin d’en analyser, par la suite, les profils.
clients_actifs <- which(is.element(clients2$client_id, id_clients3))
clients_i <- clients2[-clients_actifs,]
age <- 2023-clients_i$birth
clients_i <- data.frame(clients_i, age)
head(clients_i)
## client_id sex birth age
## 802 c_8253 f 2001 22
## 2484 c_3789 f 1997 26
## 2735 c_4406 f 1998 25
## 2770 c_2706 f 1967 56
## 2852 c_3443 m 1959 64
## 3180 c_4447 m 1956 67
library(magrittr)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
clients_inactifs <- clients_i %>% group_by(sex) %>% summarise(nb = n(), prop = round(nb/21*100, digits = 2), age_moyen = round(sum(age)/nb, digits = 2))
clients_inactifs_age <- clients_i %>% group_by(age) %>% summarise(nb = n(), prop = round(nb/21*100, digits = 2))
head(clients_inactifs)
## # A tibble: 2 × 4
## sex nb prop age_moyen
## <chr> <int> <dbl> <dbl>
## 1 f 11 52.4 38.1
## 2 m 10 47.6 39.2
head(clients_inactifs_age)
## # A tibble: 6 × 3
## age nb prop
## <dbl> <int> <dbl>
## 1 19 3 14.3
## 2 20 1 4.76
## 3 21 1 4.76
## 4 22 2 9.52
## 5 24 1 4.76
## 6 25 1 4.76
library(ggplot2)
library(hrbrthemes)
## NOTE: Either Arial Narrow or Roboto Condensed fonts are required to use these themes.
## Please use hrbrthemes::import_roboto_condensed() to install Roboto Condensed and
## if Arial Narrow is not on your system, please see https://bit.ly/arialnarrow
ggplot(clients_inactifs, aes(x=sex, y=age_moyen)) +
geom_bar(stat = "identity", width=0.5) +
ylab("Âge moyen") +
xlab("Sexe") +
ggtitle("Âge moyen des clients inactifs en fonction du sexe") +
theme_ipsum() +
coord_flip()
library(ggplot2)
library(hrbrthemes)
ggplot(clients_inactifs_age, aes(x=nb, y=age, fill=nb)) +
ggtitle("Répartition des clients inactifs en fonction de leur âge") +
xlab("Nombre de personnes") +
ylab("Âge des clients") +
theme_ipsum() +
geom_violin()
library(ggplot2)
clients_inactifs$ymax <- cumsum(clients_inactifs$prop)
clients_inactifs$ymin <- c(0, head(clients_inactifs$ymax, n=-1))
clients_inactifs$labelPosition <- (clients_inactifs$ymax + clients_inactifs$ymin) / 2
clients_inactifs$label <- paste0(clients_inactifs$sex, "\n proportion(en %): \n", clients_inactifs$prop)
ggplot(clients_inactifs, aes(ymax=ymax, ymin=ymin, xmax=4, xmin=3, fill=sex)) +
geom_rect() +
geom_label( x=3.5, aes(y=labelPosition, label=label), size=6) +
scale_fill_brewer(palette=4) +
coord_polar(theta="y") +
xlim(c(2, 4)) +
ggtitle("Répartition des clients inactifs en fonction du sexe") +
theme_void() +
theme(legend.position = "none")
Nous pouvons maintenant continuer en n’utilisant que les clients actifs :
clients2 <- clients2[is.element (clients2$client_id, id_clients3),]
head(clients2)
## client_id sex birth
## 1 c_4410 f 1967
## 2 c_7839 f 1975
## 3 c_1699 f 1984
## 4 c_5961 f 1962
## 5 c_5320 m 1943
## 6 c_415 m 1993
id_prod1 <- unique(prod$id_prod)
id_prod2 <- unique(trans$id_prod)
id_prod3 <- intersect(id_prod1, id_prod2)
21 références présentes dans la table des produits n’ont jamais été achetées. Isolons-les également afin d’en analyser, par la suite, les caractéristiques :
ref_vendues <- which(is.element(prod$id_prod, id_prod3))
ref_invendues <- prod[-ref_vendues,]
head(ref_invendues)
## id_prod price categ
## 185 0_1016 35.06 0
## 280 0_1780 1.67 0
## 738 0_1062 20.08 0
## 795 0_1119 2.99 0
## 812 0_1014 1.15 0
## 847 1_0 31.82 1
Commençons par classer les références invendues en fonction de leurs catégories :
library(magrittr)
library(dplyr)
ref_invendues_categ <- ref_invendues %>% group_by(categ) %>% summarise(nb = n(), prop = round(nb/21*100, digits = 2), prix_moyen = round(sum(price)/nb, digits = 2))
head(ref_invendues_categ)
## # A tibble: 3 × 4
## categ nb prop prix_moyen
## <fct> <int> <dbl> <dbl>
## 1 0 16 76.2 14.3
## 2 1 2 9.52 35.8
## 3 2 3 14.3 165.
Représentons graphiquement ce dataframe afin d’en faciliter la compréhension :
library(ggplot2)
library(hrbrthemes)
ggplot(ref_invendues_categ, aes(fill=categ, y=prop, x="Références")) +
geom_bar(position="fill", stat="identity") +
ylab("Proportion") +
theme_ipsum() +
ggtitle("Répartition des catégories des produits invendus")
La catégorie 0 est la plus largement représentée dans les références invendues. Intéressons nous maintenant aux prix des références invendues :
library(magrittr)
library(dplyr)
ref_invendues_price <- ref_invendues %>% group_by(categ) %>% summarise(nb = n(), prop = round(nb/21*100, digits = 2), prix_moyen = round(sum(price)/nb, digits = 2))
head(ref_invendues_price)
## # A tibble: 3 × 4
## categ nb prop prix_moyen
## <fct> <int> <dbl> <dbl>
## 1 0 16 76.2 14.3
## 2 1 2 9.52 35.8
## 3 2 3 14.3 165.
Représentons graphiquement la répartition des prix des références invendues :
library(ggplot2)
ref_invendues %>%
ggplot( aes(x=price)) +
geom_density(fill="#69b3a2", color="#e9ecef", alpha=0.8) +
xlab("Prix") +
ylab("Densité") +
theme_ipsum() +
ggtitle("Répartition des prix des références invendues")
Et avec une toute autre représentation :
library(ggplot2)
ggplot(ref_invendues, aes(x="Références", y=price)) +
geom_boxplot(fill="slateblue", alpha=0.5) +
ylab("Prix") +
theme_ipsum() +
ggtitle("Répartition des prix des références invendues")
La catégorie 0 étant la plus représentée dans cet échantillon, il n’est pas étonnant que la grosse majorité des prix soit inférieure à 50€ (la catégorie 0 ayant le prix moyen le plus faible). Qu’en est-il de la répartition des prix par catégorie ?
library(ggplot2)
ggplot(ref_invendues, aes(x=as.factor(categ), y=price)) +
geom_boxplot(fill="slateblue", alpha=0.2) +
xlab("Catégorie") +
ylab("Prix") +
theme_ipsum() +
ggtitle("Répartition des prix par catégorie")
Poursuivons maintenant en utilisant uniquement les références vendues :
prod <- prod[is.element (prod$id_prod, id_prod3),]
doublons_c <- sum(duplicated(clients2$client_id))
doublons_p <- sum(duplicated(prod$id_prod))
doublons_t <- sum(duplicated(trans$session_id))
Nous n’avons pas de doublons dans les dataframes “prod” et “clients”. En ce qui concerne les transactions, nous n’avons pas de clé primaire relative à celles-ci et il est raisonnable d’avoir des doublons au niveau des session_id dans la mesure où plusieurs transactions peuvent intervenir lors d’une même session.
na_p <- which(is.na(prod))
na_c <- which(is.na(clients2))
na_t <- which(is.na(trans))
na_p
## integer(0)
na_c
## integer(0)
na_t
## integer(0)
Nous n’avons pas de NA ✓.
Commençons par vérifier la classe des dates que nous avons :
str(trans$date)
## chr [1:679332] "2022-05-20 13:21:29.043970" "2022-02-02 07:55:19.149409" ...
Convertissons la chaîne de charactère en date afin de faciliter la manipulation de celles-ci :
trans$date <- as.Date(trans$date)
Assurons nous que le changement a bien été effectué :
str(trans$date)
## Date[1:679332], format: "2022-05-20" "2022-02-02" "2022-06-18" "2021-06-24" "2023-01-11" ...
Changement opéré ✓.
df1 <- merge(trans, prod, all = T)
head(df1)
## id_prod date session_id client_id price categ
## 1 0_0 2022-02-22 s_169315 c_1494 3.75 0
## 2 0_0 2021-10-29 s_111848 c_2068 3.75 0
## 3 0_0 2022-06-22 s_227677 c_3454 3.75 0
## 4 0_0 2022-10-28 s_289299 c_1126 3.75 0
## 5 0_0 2022-11-22 s_301230 c_803 3.75 0
## 6 0_0 2022-02-08 s_162168 c_3172 3.75 0
Nous avons opté pour une jointure externe afin de conserver l’intégralité des lignes de nos dataframes. Vérifions maintenant si nous avons des NAs dans ce nouveau dataframe, et si oui, où ils se trouvent :
summary(df1)
## id_prod date session_id client_id
## Length:679332 Min. :2021-03-01 Length:679332 Length:679332
## Class :character 1st Qu.:2021-09-08 Class :character Class :character
## Mode :character Median :2022-03-03 Mode :character Mode :character
## Mean :2022-03-03
## 3rd Qu.:2022-08-30
## Max. :2023-02-28
##
## price categ
## Min. : 0.62 0 :415459
## 1st Qu.: 8.87 1 :227169
## Median : 13.99 2 : 36483
## Mean : 17.45 NA's: 221
## 3rd Qu.: 18.99
## Max. :300.00
## NA's :221
Nous avons des données manquantes au niveau des prix et des catégories. Étant donné que nous avions préalablement vérifié s’il y avait des NAs dans nos différentes tables, nous pouvons supposer que la table des transactions contenait un id_prod qui n’est pas présent dans la table des produits et qui s’est retrouvé dans df1 suite à la jointure. Vérifions cette hypothèse :
id_prod21 <- unique(df1$id_prod)
id_prod22 <- unique(prod$id_prod)
id_prod23 <- intersect(id_prod1, id_prod2)
non_na <- which(is.element(df1$id_prod, id_prod23))
na <- df1[-non_na,]
Nous avons effectivement un id_produit présent dans df1 mais pas dans la table des produits et au vue de sa syntaxe, nous pouvons conclure qu’il appartient à la catégorie 0. Nous allons donc remplacer les NAs par la catégorie 0 et par le prix moyen constaté pour cette même catégorie :
pm_0 <- mean(produits[(produits$categ == 0),]$price)
pm_0
## [1] 11.72728
df1$price[df1$id_prod=="0_2245"] <- pm_0
df1$categ[df1$id_prod=="0_2245"] <- 0
Vérifions qu’il n’y a plus de NAs au niveau des prix et des catégories :
summary(df1)
## id_prod date session_id client_id
## Length:679332 Min. :2021-03-01 Length:679332 Length:679332
## Class :character 1st Qu.:2021-09-08 Class :character Class :character
## Mode :character Median :2022-03-03 Mode :character Mode :character
## Mean :2022-03-03
## 3rd Qu.:2022-08-30
## Max. :2023-02-28
## price categ
## Min. : 0.62 0:415680
## 1st Qu.: 8.87 1:227169
## Median : 13.99 2: 36483
## Mean : 17.45
## 3rd Qu.: 18.99
## Max. :300.00
C’est parfait ✓.
clients2$age <- 2023-clients2$birth
data <- merge(df1, clients2)
head(data)
## client_id id_prod date session_id price categ sex birth age
## 1 c_1 0_1378 2021-08-23 s_79696 13.96 0 m 1955 68
## 2 c_1 0_1090 2021-12-19 s_136532 13.78 0 m 1955 68
## 3 c_1 0_1547 2021-09-08 s_86739 8.99 0 m 1955 68
## 4 c_1 1_713 2021-11-15 s_120172 33.99 1 m 1955 68
## 5 c_1 1_364 2022-06-15 s_224447 10.30 1 m 1955 68
## 6 c_1 0_2277 2021-09-06 s_85977 10.99 0 m 1955 68
Afin de faciliter la manipulation des données, décomposons les dates de notre dataframe :
library(lubridate)
##
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union
library(zoo)
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
data$date <- ymd(data$date)
data$annee_mois <- data$date
data$annee_mois <- format(data$annee_mois, "%Y-%m")
data$annee_mois <- ym(data$annee_mois)
data$jour <- mday(data$date)
data$mois <- month(data$date)
data$annee <- year(data$date)
head(data)
## client_id id_prod date session_id price categ sex birth age annee_mois
## 1 c_1 0_1378 2021-08-23 s_79696 13.96 0 m 1955 68 2021-08-01
## 2 c_1 0_1090 2021-12-19 s_136532 13.78 0 m 1955 68 2021-12-01
## 3 c_1 0_1547 2021-09-08 s_86739 8.99 0 m 1955 68 2021-09-01
## 4 c_1 1_713 2021-11-15 s_120172 33.99 1 m 1955 68 2021-11-01
## 5 c_1 1_364 2022-06-15 s_224447 10.30 1 m 1955 68 2022-06-01
## 6 c_1 0_2277 2021-09-06 s_85977 10.99 0 m 1955 68 2021-09-01
## jour mois annee
## 1 23 8 2021
## 2 19 12 2021
## 3 8 9 2021
## 4 15 11 2021
## 5 15 6 2022
## 6 6 9 2021
Nous venons d’ajouter des colonnes représentant les éléments qui composent les dates (jours, mois et années). Vérifions une nouvelle fois si nous avons des NAs :
summary(data)
## client_id id_prod date session_id
## Length:679332 Length:679332 Min. :2021-03-01 Length:679332
## Class :character Class :character 1st Qu.:2021-09-08 Class :character
## Mode :character Mode :character Median :2022-03-03 Mode :character
## Mean :2022-03-03
## 3rd Qu.:2022-08-30
## Max. :2023-02-28
## price categ sex birth age
## Min. : 0.62 0:415680 Length:679332 Min. :1929 Min. :19.00
## 1st Qu.: 8.87 1:227169 Class :character 1st Qu.:1970 1st Qu.:36.00
## Median : 13.99 2: 36483 Mode :character Median :1980 Median :43.00
## Mean : 17.45 Mean :1978 Mean :45.19
## 3rd Qu.: 18.99 3rd Qu.:1987 3rd Qu.:53.00
## Max. :300.00 Max. :2004 Max. :94.00
## annee_mois jour mois annee
## Min. :2021-03-01 Min. : 1.00 Min. : 1.000 Min. :2021
## 1st Qu.:2021-09-01 1st Qu.: 8.00 1st Qu.: 3.000 1st Qu.:2021
## Median :2022-03-01 Median :16.00 Median : 6.000 Median :2022
## Mean :2022-02-16 Mean :15.76 Mean : 6.504 Mean :2022
## 3rd Qu.:2022-08-01 3rd Qu.:23.00 3rd Qu.: 9.000 3rd Qu.:2022
## Max. :2023-02-01 Max. :31.00 Max. :12.000 Max. :2023
Rien à signaler.
ca_total <- round(sum(data$price), digits = 2)
ca_total
## [1] 11856320
nt_ventes <- length(data$session_id)
nt_ventes
## [1] 679332
panier_moyen <- mean(data$price)
panier_moyen
## [1] 17.45291
Le chiffre d’affaires global du site s’élève à environ 11 856 318€ sur un total de 679 332 transactions, soit un montant moyen de 17,45€ par transaction.
library(magrittr)
library(dplyr)
data_per_year_c <- data %>% group_by(annee) %>% summarise(ca = sum(price), nb_ventes = n())
data_per_year_c
## # A tibble: 3 × 3
## annee ca nb_ventes
## <dbl> <dbl> <int>
## 1 2021 4771847. 278335
## 2 2022 6110089. 346500
## 3 2023 974384. 54497
2022 étant la seule année civile complète de notre dataframe, il n’est pas surprenant que ce soit l’année ayant généré le plus de chiffre d’affaires et de ventes. Intéressons-nous donc plutôt aux ventes mensuelles.
Nous allons maintenant calculer le chiffre d’affaires classé par mois :
library(magrittr)
library(dplyr)
library(tsibble)
##
## Attaching package: 'tsibble'
## The following object is masked from 'package:zoo':
##
## index
## The following object is masked from 'package:lubridate':
##
## interval
## The following objects are masked from 'package:base':
##
## intersect, setdiff, union
data_per_month <- unique(data %>% group_by(annee_mois) %>% summarise(annee=year(annee_mois), mois=month(annee_mois), ca = sum(price), nb_ventes = n()))
## `summarise()` has grouped output by 'annee_mois'. You can override using the
## `.groups` argument.
data_per_month$annee_mois <- yearmonth(data_per_month$annee_mois)
head(data_per_month)
## # A tibble: 6 × 5
## # Groups: annee_mois [6]
## annee_mois annee mois ca nb_ventes
## <mth> <dbl> <dbl> <dbl> <int>
## 1 2021 Mar 2021 3 482546. 28610
## 2 2021 Apr 2021 4 476273. 28457
## 3 2021 May 2021 5 493037. 28293
## 4 2021 Jun 2021 6 484171. 26857
## 5 2021 Jul 2021 7 482882. 24742
## 6 2021 Aug 2021 8 482390. 25659
Représentons graphiquement ce dataframe afin de pouvoir observer l’évolution du chiffre d’affaires au cours des mois :
library(magrittr)
library(ggplot2)
library(hrbrthemes)
data_per_month %>%
tail(24) %>%
ggplot(aes(x=annee_mois, y=ca, ymin=0, ymax=700000)) +
geom_line(color="grey") +
geom_point(shape=21, color="black", fill="#3398FF", size=3) +
xlab("Mois") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Évolution mensuelle du chiffre d'affaires")
Jetons également un oeil à l’évolution du montant du panier moyen au cours des mois :
library(magrittr)
library(ggplot2)
library(hrbrthemes)
data_per_month %>%
tail(24) %>%
ggplot(aes(x=annee_mois, y=ca/nb_ventes, ymin=0, ymax=25)) +
geom_line(color="grey") +
geom_point(shape=21, color="black", fill="#3398FF", size=3) +
xlab("Mois") +
ylab("Montant du panier moyen") +
theme_ipsum() +
ggtitle("Évolution mensuelle du panier moyen")
Nous pouvons observer que le chiffre d’affaires et le montant du panier moyen ont connu une baisse au cours du mois d’octobre 2021. Essayons de comprendre à quoi peuvent être dûes ces importantes diminutions :
library(dplyr)
library(magrittr)
data_per_month_categ <- data %>% group_by(categ, annee_mois) %>% summarise(ca=sum(price), nb_ventes=n())
## `summarise()` has grouped output by 'categ'. You can override using the
## `.groups` argument.
head(data_per_month_categ)
## # A tibble: 6 × 4
## # Groups: categ [1]
## categ annee_mois ca nb_ventes
## <fct> <date> <dbl> <int>
## 1 0 2021-03-01 193735. 18140
## 2 0 2021-04-01 205387. 19356
## 3 0 2021-05-01 196281. 18509
## 4 0 2021-06-01 168025. 15905
## 5 0 2021-07-01 144798. 13582
## 6 0 2021-08-01 167843. 15737
Représentons ces résultats graphiquement afin de mieux les analyser :
library(magrittr)
library(ggplot2)
library(hrbrthemes)
ggplot(data_per_month_categ, aes(fill=categ, y=ca, x=annee_mois)) +
geom_bar(stat="identity", position=position_dodge2()) +
xlab("Mois") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Répartition du chiffre d'affaires mensuel par catégorie")
library(magrittr)
library(ggplot2)
library(hrbrthemes)
ggplot(data_per_month_categ, aes(fill=categ, y=nb_ventes, x=annee_mois)) +
geom_bar(stat="identity", position=position_dodge2()) +
xlab("Mois") +
ylab("Nombre de ventes") +
theme_ipsum() +
ggtitle("Répartition des ventes mensuelles par catégorie")
Nous pouvons clairement remarquer que les ventes de livres de la catégorie 1 ont subi une forte baisse au mois d’octobre 2021, baisse qui ne se retrouve pas plus tard. Il doit y avoir un problème au niveau des données qui ont été enregistrées.
Penchons-nous plus particulièrement sur le mois d’octobre 2021 et sur les transactions qui ont été enregistrées sur cette période :
library(magrittr)
library(dplyr)
ventes_oct21 <- data[(data$mois == "10" & data$annee == "2021"),] %>% group_by(categ, jour) %>% summarise(ca=sum(price), nb_ventes=n())
## `summarise()` has grouped output by 'categ'. You can override using the
## `.groups` argument.
head(ventes_oct21)
## # A tibble: 6 × 4
## # Groups: categ [1]
## categ jour ca nb_ventes
## <fct> <int> <dbl> <int>
## 1 0 1 6950. 663
## 2 0 2 7141. 661
## 3 0 3 6787. 648
## 4 0 4 6557. 603
## 5 0 5 6358. 594
## 6 0 6 7547. 702
Représentons ces données graphiquement en groupant par catégorie :
library(magrittr)
library(dplyr)
library(ggplot2)
library(graphics)
par(mfrow=c(3,1))
ventes_oct21 %>%
filter(categ == "0") %>%
ggplot(aes(x=jour, y=nb_ventes)) +
geom_bar(stat = "identity", width=0.5, color="grey", fill="lightblue") +
xlab("Jour") +
ylab("Nombre de ventes") +
ggtitle("Ventes enregistrées en octobre 2021 (catégorie 0)") +
theme_ipsum()
ventes_oct21 %>%
filter(categ == "1") %>%
ggplot(aes(x=jour, y=nb_ventes)) +
geom_bar(stat = "identity", width=0.5, color="grey", fill="blue") +
xlab("Jour") +
ylab("Nombre de ventes") +
ggtitle("Ventes enregistrées en octobre 2021 (catégorie 1)") +
theme_ipsum()
ventes_oct21 %>%
filter(categ == "2") %>%
ggplot(aes(x=jour, y=nb_ventes)) +
geom_bar(stat = "identity", width=0.5, color="grey", fill="darkblue") +
xlab("Jour") +
ylab("Nombre de ventes") +
ggtitle("Ventes enregistrées en octobre 2021 (catégorie 2)") +
theme_ipsum()
Aucune transaction n’a été enregistrée pour les livres de la catégorie 1 entre le 1er et le 28 octobre 2021 (ce qui est probablement dû à un problème d’acquisition des données), d’où la baisse significative de chiffre d’affaires sur ce mois.
Commençons par classer nos données par catégorie :
library(dplyr)
library(magrittr)
data_per_cat <- data %>% group_by(categ) %>% summarise(ca = sum(price), prix_moyen = round(mean(price), digits = 2), prop_ca = round(ca/ca_total*100, digits = 2), nb_ventes = n(), prop_ventes = round(nb_ventes/679332*100, digits = 2))
head(data_per_cat)
## # A tibble: 3 × 6
## categ ca prix_moyen prop_ca nb_ventes prop_ventes
## <fct> <dbl> <dbl> <dbl> <int> <dbl>
## 1 0 4422323. 10.6 37.3 415680 61.2
## 2 1 4653723. 20.5 39.2 227169 33.4
## 3 2 2780275. 76.2 23.4 36483 5.37
Représentons graphiquement les répartitions de chiffres d’affaires et ventes par catégorie :
library(magrittr)
library(ggplot2)
library(hrbrthemes)
library(graphics)
par(mfrow=c(2,1))
data_per_cat %>%
ggplot(aes(x="", y=prop_ca, fill=categ)) +
geom_bar(stat="identity", width=1, color="white") +
coord_polar("y", start=0) +
theme_void() +
ggtitle("Chiffre d'affaires par catégorie")
data_per_cat %>%
ggplot(aes(x="", y=prop_ventes, fill=categ)) +
geom_bar(stat="identity", width=1, color="white") +
coord_polar("y", start=0) +
theme_void() +
ggtitle("Ventes par catégorie")
La catégorie la plus vendue est la catégorie 0 alors que la moins vendue est la catégorie 2. En ce qui concerne la répartition du chiffre d’affaires, elle est beaucoup plus équilibrée que la répartition des ventes (cette différence est dûe aux écarts de prix constatés entre les catégories).
Créons un dataframe nous permettant d’obtenir les ventes et chiffre d’affaires quotidiens :
library(magrittr)
library(dplyr)
data_per_date <- data %>% group_by(date, annee, mois, jour) %>% summarise(ca = sum(price), nb_ventes = n())
## `summarise()` has grouped output by 'date', 'annee', 'mois'. You can override
## using the `.groups` argument.
data_per_date$annee <- as.factor(data_per_date$annee)
head(data_per_date)
## # A tibble: 6 × 6
## # Groups: date, annee, mois [6]
## date annee mois jour ca nb_ventes
## <date> <fct> <dbl> <int> <dbl> <int>
## 1 2021-03-01 2021 3 1 16577. 963
## 2 2021-03-02 2021 3 2 15498. 940
## 3 2021-03-03 2021 3 3 15199. 911
## 4 2021-03-04 2021 3 4 15196. 903
## 5 2021-03-05 2021 3 5 17471. 943
## 6 2021-03-06 2021 3 6 15785. 961
Comparons maintenant les chiffres d’affaires réalisés chaque mois sur les années N-1 et N :
library(magrittr)
library(dplyr)
library(ggplot2)
library(graphics)
par(mfrow=c(3,4))
data_per_date[(data_per_date$mois == "3"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de mars 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "4"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois d'avril 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "5"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de mai 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "6"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de juin 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "7"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de juillet 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "8"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois d'août 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "9"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de septembre 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "10"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois d'octobre 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "11"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de novembre 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "12"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de décembre 2021 et 2022") +
geom_line()
data_per_date[(data_per_date$mois == "1"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de janvier 2022 et 2023") +
geom_line()
data_per_date[(data_per_date$mois == "2"),] %>%
ggplot( aes(x=jour, y=ca, group=annee, color=annee)) +
xlab("Jour") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des mois de février 2022 et 2023") +
geom_line()
Faisons de même pour l’intégralité des années N-1 et N :
library(magrittr)
library(dplyr)
library(ggplot2)
library(graphics)
n_mois <- rep(c("01-Mar","02-Apr","03-May","04-Jun","05-Jul","06-Aug","07-Sep","08-Oct","09-Nov","10-Dec","11-Jan","12-Feb"),2)
data_per_month$n_mois <- n_mois
n_annee <- rep(c("Année 1", "Année 2"), each=12)
data_per_month$n_annee <- n_annee
data_per_month %>%
ggplot(aes(x=n_mois, y=ca, group=n_annee, color=n_annee)) +
xlab("Mois") +
ylab("Chiffre d'affaires") +
theme_ipsum() +
ggtitle("Ventes des années 2021 et 2022 (années glissantes)") +
geom_line()
Nous pouvons observer que le chiffre d’affaires est relativement stable au cours de l’année et ne semble pas connaitre de phénomène de saisonnalité.
Commençons par calculer le chiffre d’affaires par client :
library(magrittr)
library(dplyr)
ca_per_client <- unique(data %>% group_by(client_id) %>% summarise(age=2023-birth, ca=sum(price), panier_moyen = round(mean(price), digits = 2), nb_achats = n()))
## `summarise()` has grouped output by 'client_id'. You can override using the
## `.groups` argument.
ca_per_client <- arrange(ca_per_client, desc(ca_per_client$ca))
lc_ca_client <- as.vector(cumsum(sort(ca_per_client$ca))/sum(ca_per_client$ca))
library(ineq)
lorenz_curve <- Lc(lc_ca_client, n=rep(1,8600), plot=FALSE)
plot(lorenz_curve, xlab="Parts cumulées des achats", ylab="Parts cumulées du chiffre d'affaires", main="Répartition du chiffre d'affaires par client")
library(DescTools)
## Registered S3 methods overwritten by 'DescTools':
## method from
## lines.Lc ineq
## plot.Lc ineq
##
## Attaching package: 'DescTools'
## The following objects are masked from 'package:ineq':
##
## Atkinson, Gini, Herfindahl, Lc, Rosenbluth
Gini(lc_ca_client, n=rep(1,8600))
## [1] 0.5035666
head(ca_per_client, n=10L)
## # A tibble: 10 × 5
## # Groups: client_id [10]
## client_id age ca panier_moyen nb_achats
## <chr> <dbl> <dbl> <dbl> <int>
## 1 c_1609 43 324033. 12.7 25488
## 2 c_4958 24 289760. 55.8 5195
## 3 c_6714 55 153669. 16.7 9187
## 4 c_3454 54 113673. 16.8 6773
## 5 c_3263 38 5277. 13.1 403
## 6 c_1570 44 5272. 14.3 369
## 7 c_2899 29 5214. 49.7 105
## 8 c_2140 46 5209. 13.0 402
## 9 c_7319 49 5156. 13.9 371
## 10 c_8026 45 5094. 13.5 377
À en juger par le montant du chiffre d’affaires des 4 plus gros acheteurs ainsi que leurs nombres de commandes, nous pouvons supposer qu’il s’agisse de revendeurs. Il serait judicieux de leur proposer un accompagnement personnalisé dans la mesure où leurs besoins seront différents des besoins de clients particuliers.
library(dplyr)
library(magrittr)
mean(produits[(produits$categ == "0"),]$price)
## [1] 11.72728
mean(produits[(produits$categ == "1"),]$price)
## [1] 25.53142
mean(produits[(produits$categ == "2"),]$price)
## [1] 108.3547
Comme nous l’avions déjà constaté en comparant la répartition du chiffre d’afffaires ainsi que celle des ventes entre les différentes catégories, les écarts de prix moyens entre celles-ci sont plûtot importants (notamment entre les catégories 1 et 2 et la catégorie 3).
library(dplyr)
library(magrittr)
data_per_prod <- data %>% group_by(id_prod) %>% summarise(nb_ventes=n())
library(dplyr)
top <- arrange(data_per_prod, desc(data_per_prod$nb_ventes))
head(top, n=10L)
## # A tibble: 10 × 2
## id_prod nb_ventes
## <chr> <int>
## 1 1_369 2252
## 2 1_417 2189
## 3 1_414 2180
## 4 1_498 2128
## 5 1_425 2096
## 6 1_403 1960
## 7 1_412 1951
## 8 1_413 1945
## 9 1_406 1939
## 10 1_407 1935
Les 10 références les plus vendues appartiennent toutes à la catégorie 1.
library(dplyr)
flop <- arrange(data_per_prod, data_per_prod$nb_ventes)
head(flop, n=10L)
## # A tibble: 10 × 2
## id_prod nb_ventes
## <chr> <int>
## 1 0_1151 1
## 2 0_1284 1
## 3 0_1379 1
## 4 0_1498 1
## 5 0_1539 1
## 6 0_1601 1
## 7 0_1633 1
## 8 0_1683 1
## 9 0_1728 1
## 10 0_2201 1
Les 10 références les moins vendues, quant à elles, appartiennent toutes à la catégorie 0.
Commençons par créer de nouveaux dataframes en ne sélectionnant que les colonnes qui nous intéressent :
library(dplyr)
dpm <- subset(data_per_month, select=c("annee_mois","ca","nb_ventes"))
head(dpm)
## # A tibble: 6 × 3
## # Groups: annee_mois [6]
## annee_mois ca nb_ventes
## <mth> <dbl> <int>
## 1 2021 Mar 482546. 28610
## 2 2021 Apr 476273. 28457
## 3 2021 May 493037. 28293
## 4 2021 Jun 484171. 26857
## 5 2021 Jul 482882. 24742
## 6 2021 Aug 482390. 25659
dpd <- subset(data_per_date, select=c("date", "ca", "nb_ventes"))
head(dpd)
## # A tibble: 6 × 3
## # Groups: date [6]
## date ca nb_ventes
## <date> <dbl> <int>
## 1 2021-03-01 16577. 963
## 2 2021-03-02 15498. 940
## 3 2021-03-03 15199. 911
## 4 2021-03-04 15196. 903
## 5 2021-03-05 17471. 943
## 6 2021-03-06 15785. 961
library(stats)
dpm_ts <- ts(dpm, frequency = 12)
decompose(dpm_ts)
## $x
## annee_mois ca nb_ventes
## Jan 1 614 482546.2 28610
## Feb 1 615 476273.5 28457
## Mar 1 616 493037.3 28293
## Apr 1 617 484170.7 26857
## May 1 618 482882.3 24742
## Jun 1 619 482390.3 25659
## Jul 1 620 507381.4 33326
## Aug 1 621 320880.8 21606
## Sep 1 622 516285.0 28321
## Oct 1 623 525999.4 32464
## Nov 1 624 525397.6 29348
## Dec 1 625 535700.5 29605
## Jan 2 626 515585.5 29707
## Feb 2 627 493163.1 27616
## Mar 2 628 517320.2 29991
## Apr 2 629 496098.2 28511
## May 2 630 510923.8 28682
## Jun 2 631 506561.1 28552
## Jul 2 632 494220.1 28315
## Aug 2 633 508035.0 28974
## Sep 2 634 496793.9 28574
## Oct 2 635 510289.9 28625
## Nov 2 636 517622.6 28945
## Dec 2 637 456761.9 25552
##
## $seasonal
## Jan Feb Mar Apr May Jun
## 1 6856.2207 -3764.2193 2645.3169 -4383.3226 1000.6464 769.3049
## 2 6856.2207 -3764.2193 2645.3169 -4383.3226 1000.6464 769.3049
## 3 6856.2207 -3764.2193 2645.3169 -4383.3226 1000.6464 769.3049
## 4 6856.2207 -3764.2193 2645.3169 -4383.3226 1000.6464 769.3049
## 5 6856.2207 -3764.2193 2645.3169 -4383.3226 1000.6464 769.3049
## 6 6856.2207 -3764.2193 2645.3169 -4383.3226 1000.6464 769.3049
## Jul Aug Sep Oct Nov Dec
## 1 8734.4704 -58036.0692 8753.2438 12822.8872 10950.8182 13650.7026
## 2 8734.4704 -58036.0692 8753.2438 12822.8872 10950.8182 13650.7026
## 3 8734.4704 -58036.0692 8753.2438 12822.8872 10950.8182 13650.7026
## 4 8734.4704 -58036.0692 8753.2438 12822.8872 10950.8182 13650.7026
## 5 8734.4704 -58036.0692 8753.2438 12822.8872 10950.8182 13650.7026
## 6 8734.4704 -58036.0692 8753.2438 12822.8872 10950.8182 13650.7026
##
## $trend
## [,1] [,2] [,3]
## Jan 1 NA NA NA
## Feb 1 NA NA NA
## Mar 1 NA NA NA
## Apr 1 NA NA NA
## May 1 NA NA NA
## Jun 1 NA NA NA
## Jul 1 620 487455.4 28153.04
## Aug 1 621 489535.8 28163.71
## Sep 1 622 491251.3 28199.42
## Oct 1 623 492760.1 28339.08
## Nov 1 624 494425.4 28572.17
## Dec 1 625 496600.9 28856.87
## Jan 2 626 497059.7 28768.62
## Feb 2 627 504309.4 28866.83
## Mar 2 628 511295.3 29184.37
## Apr 2 629 509828.7 29034.96
## May 2 630 508850.1 28858.21
## Jun 2 631 505237.1 28672.54
## Jul 2 NA NA NA
## Aug 2 NA NA NA
## Sep 2 NA NA NA
## Oct 2 NA NA NA
## Nov 2 NA NA NA
## Dec 2 NA NA NA
##
## $random
## x - seasonal.x.annee_mois x - seasonal.x.ca x - seasonal.x.nb_ventes
## Jan 1 NA NA NA
## Feb 1 NA NA NA
## Mar 1 NA NA NA
## Apr 1 NA NA NA
## May 1 NA NA NA
## Jun 1 NA NA NA
## Jul 1 -8734.4704 11191.5497 -3561.5120
## Aug 1 58036.0692 -110618.8627 51478.3609
## Sep 1 -8753.2438 16280.4716 -8631.6605
## Oct 1 -12822.8872 20416.4252 -8697.9706
## Nov 1 -10950.8182 20021.3705 -10174.9849
## Dec 1 -13650.7026 25448.8477 -12902.5776
## Jan 2 -6856.2207 11669.6338 -5917.8457
## Feb 2 3764.2193 -7382.0378 2513.3859
## Mar 2 -2645.3169 3379.5761 -1838.6919
## Apr 2 4383.3226 -9347.1195 3859.3643
## May 2 -1000.6464 1073.0684 -1176.8547
## Jun 2 -769.3049 554.7189 -889.8466
## Jul 2 NA NA NA
## Aug 2 NA NA NA
## Sep 2 NA NA NA
## Oct 2 NA NA NA
## Nov 2 NA NA NA
## Dec 2 NA NA NA
##
## $figure
## [1] 6856.2207 -3764.2193 2645.3169 -4383.3226 1000.6464 769.3049
## [7] 8734.4704 -58036.0692 8753.2438 12822.8872 10950.8182 13650.7026
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"
plot(dpm_ts)
library(zoo)
rollmean(dpm_ts, 3)
## annee_mois ca nb_ventes
## Feb 1 615 483952.3 28453.33
## Mar 1 616 484493.8 27869.00
## Apr 1 617 486696.7 26630.67
## May 1 618 483147.8 25752.67
## Jun 1 619 490884.7 27909.00
## Jul 1 620 436884.2 26863.67
## Aug 1 621 448182.4 27751.00
## Sep 1 622 454388.4 27463.67
## Oct 1 623 522560.7 30044.33
## Nov 1 624 529032.5 30472.33
## Dec 1 625 525561.2 29553.33
## Jan 2 626 514816.4 28976.00
## Feb 2 627 508689.6 29104.67
## Mar 2 628 502193.9 28706.00
## Apr 2 629 508114.1 29061.33
## May 2 630 504527.7 28581.67
## Jun 2 631 503901.7 28516.33
## Jul 2 632 502938.7 28613.67
## Aug 2 633 499683.0 28621.00
## Sep 2 634 505039.6 28724.33
## Oct 2 635 508235.5 28714.67
## Nov 2 636 494891.5 27707.33
plot(rollmean(dpm_ts, 3))
library(stats)
dpd_ts <- ts(dpd, frequency = 365)
decompose(dpd_ts)
## $x
## Time Series:
## Start = c(1, 1)
## End = c(2, 365)
## Frequency = 365
## date ca nb_ventes
## 1.000000 18687 16576.947 963
## 1.002740 18688 15498.177 940
## 1.005479 18689 15198.690 911
## 1.008219 18690 15196.070 903
## 1.010959 18691 17471.370 943
## 1.013699 18692 15785.280 961
## 1.016438 18693 14771.927 906
## 1.019178 18694 15679.530 928
## 1.021918 18695 15710.510 952
## 1.024658 18696 15496.870 942
## 1.027397 18697 14801.140 914
## 1.030137 18698 14448.580 888
## 1.032877 18699 14324.840 884
## 1.035616 18700 15231.770 914
## 1.038356 18701 16141.660 918
## 1.041096 18702 15971.740 945
## 1.043836 18703 16025.470 958
## 1.046575 18704 15060.790 922
## 1.049315 18705 15545.770 917
## 1.052055 18706 15853.990 945
## 1.054795 18707 17459.660 985
## 1.057534 18708 15657.050 919
## 1.060274 18709 16040.277 921
## 1.063014 18710 15101.700 880
## 1.065753 18711 15162.180 927
## 1.068493 18712 16176.280 919
## 1.071233 18713 15238.090 889
## 1.073973 18714 16100.675 916
## 1.076712 18715 14460.495 883
## 1.079452 18716 14827.237 898
## 1.082192 18717 15531.390 919
## 1.084932 18718 15520.780 916
## 1.087671 18719 15982.777 961
## 1.090411 18720 15516.037 948
## 1.093151 18721 16115.580 886
## 1.095890 18722 17472.730 983
## 1.098630 18723 16811.747 960
## 1.101370 18724 15507.217 932
## 1.104110 18725 15002.420 918
## 1.106849 18726 15749.197 925
## 1.109589 18727 15260.829 937
## 1.112329 18728 16429.510 989
## 1.115068 18729 15916.890 968
## 1.117808 18730 15594.560 916
## 1.120548 18731 15956.470 936
## 1.123288 18732 15552.730 954
## 1.126027 18733 14773.480 916
## 1.128767 18734 15836.347 941
## 1.131507 18735 14954.187 946
## 1.134247 18736 15513.760 928
## 1.136986 18737 15597.650 934
## 1.139726 18738 15404.050 922
## 1.142466 18739 17043.357 1003
## 1.145205 18740 15242.040 900
## 1.147945 18741 16572.720 968
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##
## $seasonal
## Time Series:
## Start = c(1, 1)
## End = c(6, 365)
## Frequency = 365
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## [811] -436.6571338 70.8562129 -191.5849993 773.1979231 -390.2778394
## [816] -356.6187253 -541.3677506 -2.9773147 555.1089094 361.8594615
## [821] -156.7906066 -561.3514193 -529.0671205 -684.0202869 -311.3767917
## [826] -282.2763143 666.8936309 981.3429941 163.1471676 -242.0540470
## [831] -393.0072433 68.0627567 33.9008729 -837.2494376 688.9133752
## [836] 1185.2844619 -153.0505268 -538.8485518 -252.4711894 -692.1905360
## [841] -240.2724995 -270.1509013 657.7673362 173.7200028 -294.8902346
## [846] -468.0331205 230.6063316 -161.0826090 -322.6724173 365.4214732
## [851] 21.7728430 -645.0593720 258.4381465 193.3353976 -120.8603899
## [856] 884.1133727 -345.1020794 945.7296533 451.8091693 -532.0363467
## [861] -215.0660636 136.8797355 -596.6610134 -687.7398353 -484.7143832
## [866] -64.9531686 91.0873769 -316.9195820 -343.7177556 -461.5558195
## [871] -245.5614974 -268.0170839 102.2926604 138.8762951 -533.1365360
## [876] 1316.6171261 277.7571261 -1010.2326340 229.7926902 -336.9654193
## [881] -615.4206298 -52.5157755 -237.5480154 -365.3760819 -262.9761225
## [886] -605.9091454 148.2815919 331.2981813 -233.9405584 197.8609576
## [891] 336.2655811 -302.7208780 381.3827359 103.3206330 -23.8432616
## [896] -576.7468623 -527.8658303 -491.2574650 -218.9896501 355.2569252
## [901] -526.5304380 -376.7723301 -299.0235447 788.3041722 -783.1729561
## [906] -373.6257871 212.1452083 -424.5300403 503.6110439 184.3641166
## [911] 470.5864819 -174.5668515 160.7065886 98.1592798 -115.1938966
## [916] 35.2460536 87.2512931 -391.1530605 -226.9350124 17.5623732
## [921] 291.0348664 -146.5583549 220.6812707 334.0285127 489.9150333
## [926] 395.8713919 106.9544720 487.8494309 721.3831296 305.8279838
## [931] 172.7926571 295.6284770 446.5030224 315.1378834 151.4350432
## [936] 327.8223400 822.2969403 770.2780229 1151.5571437 560.4421482
## [941] 946.1113172 806.3252416 907.0857871 826.8964014 381.9663010
## [946] -2363.3104686 -2430.2910805 -2338.5493138 -2311.5746214 -2245.1922262
## [951] -2714.7634524 -2013.0233154 -2285.5496832 -2501.3378750 -2014.8037746
## [956] -2441.8720643 -2287.8391237 -2282.4476716 -2293.5818634 -2010.6227991
## [961] -2248.1234682 -2418.2587766 -2584.8465143 -2452.3613246 -2253.7413678
## [966] -2635.5995413 -2493.1530390 -2148.2520070 -2780.8307924 -2443.6445849
## [971] -2207.7881739 -447.0011693 142.2531229 -231.8365575 113.7479905
## [976] 583.1296526 610.7232989 -76.8778377 136.7783383 288.1137904
## [981] -421.1087484 311.4958086 380.9512607 -113.4070540 566.0004529
## [986] 336.0074276 337.8071992 528.5825442 367.6848663 223.8189967
## [991] 185.3828871 502.6171976 629.3956019 -0.4617547 130.8386563
## [996] 345.7377497 411.7559257 961.9514873 337.8726994 564.4902910
## [1001] 620.9527866 209.9473412 663.2267434 394.5223690 1141.6989759
## [1006] 181.7598460 336.2010606 96.1930697 449.2136201 324.8117364
## [1011] 265.9711154 315.5586131 400.0877090 114.4128323 359.9774417
## [1016] 136.7981590 65.1526795 293.8925060 202.2204487 -4.6449643
## [1021] 276.9210033 522.2540286 181.0365126 137.3386314 209.9665126
## [1026] -36.2658369 317.5510672 412.9675969 519.3931860 371.3100079
## [1031] 357.3400079 507.4788572 501.8217248 458.2561332 213.2832980
## [1036] 979.9726770 334.9099647 60.2362910 435.1961631 362.9443524
## [1041] -81.5784487 323.6782362 63.4745923 531.5162179 -362.8363325
## [1046] 384.2975878 128.0892931 405.9864163 419.9243524 454.7450830
## [1051] 256.0091013 121.8491768 675.9358435 106.5148688 12.0128414
## [1056] 267.0218485 519.6665151 -195.4134616 141.8970431 358.6742602
## [1061] -176.4157398 194.7889244 -92.6901690 590.1318908 752.7572606
## [1066] 500.2497471 98.2719347 310.5843914 1018.8610306 647.0357272
## [1071] 1080.4631153 878.0584345 1038.9744711 925.2799115 967.7830348
## [1076] 796.9804437 1253.2338799 1248.8264802 1156.7768845 992.0259688
## [1081] 1288.2767152 1386.6658177 1205.7503930 962.7190738 929.2646786
## [1086] 769.2268978 1216.4995412 757.9039547 608.4827401 928.7185599
## [1091] 1390.3123175 644.0924063 1249.4742195 1003.9414889 882.1852033
## [1096] 286.9863748 1044.9239912 334.8216483 -561.4433654 -127.3880984
## [1101] 114.5016251 906.2141457 -104.1371511 -53.7951810 526.5592299
## [1106] -91.8330557 -564.4173795 -637.9615281 149.1544421 -256.3734733
## [1111] -343.0058934 -211.3798776 1069.9217920 -381.4790183 -107.3450822
## [1116] -684.2863267 162.4766230 709.2311685 335.6176824 991.1810132
## [1121] -129.4425733 -89.5247012 941.2128646 416.1724836 -164.4979158
## [1126] -153.4777174 -368.9902719 348.0242420 -32.7553313 -468.8374633
## [1131] 76.8147119 -195.3397472 208.4084520 -345.5514019 -520.0222238
## [1136] -189.8932632 46.4782627 -77.6852533 -309.2993604 225.7017081
## [1141] -300.4507510 -164.1428971 300.2689501 935.2895437 -344.0317556
## [1146] 53.4235138 -546.2506937 -387.3222578 770.1587401 426.6282195
## [1151] 210.6712764 -984.7331935 -197.4895704 -322.7264837 565.7853337
## [1156] 315.4718634 -411.3331802 312.2896326 -102.7591096 154.5223125
## [1161] 18.5882420 -820.3528631 10.7118700 -535.3729951 -155.2761159
## [1166] 185.7233677 253.6864321 -243.6742139 -695.1703600 -483.5787826
## [1171] 1267.3040186 1038.2479206 528.5533021 -29.9759764 -281.0326730
## [1176] -436.6571338 70.8562129 -191.5849993 773.1979231 -390.2778394
## [1181] -356.6187253 -541.3677506 -2.9773147 555.1089094 361.8594615
## [1186] -156.7906066 -561.3514193 -529.0671205 -684.0202869 -311.3767917
## [1191] -282.2763143 666.8936309 981.3429941 163.1471676 -242.0540470
## [1196] -393.0072433 68.0627567 33.9008729 -837.2494376 688.9133752
## [1201] 1185.2844619 -153.0505268 -538.8485518 -252.4711894 -692.1905360
## [1206] -240.2724995 -270.1509013 657.7673362 173.7200028 -294.8902346
## [1211] -468.0331205 230.6063316 -161.0826090 -322.6724173 365.4214732
## [1216] 21.7728430 -645.0593720 258.4381465 193.3353976 -120.8603899
## [1221] 884.1133727 -345.1020794 945.7296533 451.8091693 -532.0363467
## [1226] -215.0660636 136.8797355 -596.6610134 -687.7398353 -484.7143832
## [1231] -64.9531686 91.0873769 -316.9195820 -343.7177556 -461.5558195
## [1236] -245.5614974 -268.0170839 102.2926604 138.8762951 -533.1365360
## [1241] 1316.6171261 277.7571261 -1010.2326340 229.7926902 -336.9654193
## [1246] -615.4206298 -52.5157755 -237.5480154 -365.3760819 -262.9761225
## [1251] -605.9091454 148.2815919 331.2981813 -233.9405584 197.8609576
## [1256] 336.2655811 -302.7208780 381.3827359 103.3206330 -23.8432616
## [1261] -576.7468623 -527.8658303 -491.2574650 -218.9896501 355.2569252
## [1266] -526.5304380 -376.7723301 -299.0235447 788.3041722 -783.1729561
## [1271] -373.6257871 212.1452083 -424.5300403 503.6110439 184.3641166
## [1276] 470.5864819 -174.5668515 160.7065886 98.1592798 -115.1938966
## [1281] 35.2460536 87.2512931 -391.1530605 -226.9350124 17.5623732
## [1286] 291.0348664 -146.5583549 220.6812707 334.0285127 489.9150333
## [1291] 395.8713919 106.9544720 487.8494309 721.3831296 305.8279838
## [1296] 172.7926571 295.6284770 446.5030224 315.1378834 151.4350432
## [1301] 327.8223400 822.2969403 770.2780229 1151.5571437 560.4421482
## [1306] 946.1113172 806.3252416 907.0857871 826.8964014 381.9663010
## [1311] -2363.3104686 -2430.2910805 -2338.5493138 -2311.5746214 -2245.1922262
## [1316] -2714.7634524 -2013.0233154 -2285.5496832 -2501.3378750 -2014.8037746
## [1321] -2441.8720643 -2287.8391237 -2282.4476716 -2293.5818634 -2010.6227991
## [1326] -2248.1234682 -2418.2587766 -2584.8465143 -2452.3613246 -2253.7413678
## [1331] -2635.5995413 -2493.1530390 -2148.2520070 -2780.8307924 -2443.6445849
## [1336] -2207.7881739 -447.0011693 142.2531229 -231.8365575 113.7479905
## [1341] 583.1296526 610.7232989 -76.8778377 136.7783383 288.1137904
## [1346] -421.1087484 311.4958086 380.9512607 -113.4070540 566.0004529
## [1351] 336.0074276 337.8071992 528.5825442 367.6848663 223.8189967
## [1356] 185.3828871 502.6171976 629.3956019 -0.4617547 130.8386563
## [1361] 345.7377497 411.7559257 961.9514873 337.8726994 564.4902910
## [1366] 620.9527866 209.9473412 663.2267434 394.5223690 1141.6989759
## [1371] 181.7598460 336.2010606 96.1930697 449.2136201 324.8117364
## [1376] 265.9711154 315.5586131 400.0877090 114.4128323 359.9774417
## [1381] 136.7981590 65.1526795 293.8925060 202.2204487 -4.6449643
## [1386] 276.9210033 522.2540286 181.0365126 137.3386314 209.9665126
## [1391] -36.2658369 317.5510672 412.9675969 519.3931860 371.3100079
## [1396] 357.3400079 507.4788572 501.8217248 458.2561332 213.2832980
## [1401] 979.9726770 334.9099647 60.2362910 435.1961631 362.9443524
## [1406] -81.5784487 323.6782362 63.4745923 531.5162179 -362.8363325
## [1411] 384.2975878 128.0892931 405.9864163 419.9243524 454.7450830
## [1416] 256.0091013 121.8491768 675.9358435 106.5148688 12.0128414
## [1421] 267.0218485 519.6665151 -195.4134616 141.8970431 358.6742602
## [1426] -176.4157398 194.7889244 -92.6901690 590.1318908 752.7572606
## [1431] 500.2497471 98.2719347 310.5843914 1018.8610306 647.0357272
## [1436] 1080.4631153 878.0584345 1038.9744711 925.2799115 967.7830348
## [1441] 796.9804437 1253.2338799 1248.8264802 1156.7768845 992.0259688
## [1446] 1288.2767152 1386.6658177 1205.7503930 962.7190738 929.2646786
## [1451] 769.2268978 1216.4995412 757.9039547 608.4827401 928.7185599
## [1456] 1390.3123175 644.0924063 1249.4742195 1003.9414889 882.1852033
## [1461] 286.9863748 1044.9239912 334.8216483 -561.4433654 -127.3880984
## [1466] 114.5016251 906.2141457 -104.1371511 -53.7951810 526.5592299
## [1471] -91.8330557 -564.4173795 -637.9615281 149.1544421 -256.3734733
## [1476] -343.0058934 -211.3798776 1069.9217920 -381.4790183 -107.3450822
## [1481] -684.2863267 162.4766230 709.2311685 335.6176824 991.1810132
## [1486] -129.4425733 -89.5247012 941.2128646 416.1724836 -164.4979158
## [1491] -153.4777174 -368.9902719 348.0242420 -32.7553313 -468.8374633
## [1496] 76.8147119 -195.3397472 208.4084520 -345.5514019 -520.0222238
## [1501] -189.8932632 46.4782627 -77.6852533 -309.2993604 225.7017081
## [1506] -300.4507510 -164.1428971 300.2689501 935.2895437 -344.0317556
## [1511] 53.4235138 -546.2506937 -387.3222578 770.1587401 426.6282195
## [1516] 210.6712764 -984.7331935 -197.4895704 -322.7264837 565.7853337
## [1521] 315.4718634 -411.3331802 312.2896326 -102.7591096 154.5223125
## [1526] 18.5882420 -820.3528631 10.7118700 -535.3729951 -155.2761159
## [1531] 185.7233677 253.6864321 -243.6742139 -695.1703600 -483.5787826
## [1536] 1267.3040186 1038.2479206 528.5533021 -29.9759764 -281.0326730
## [1541] -436.6571338 70.8562129 -191.5849993 773.1979231 -390.2778394
## [1546] -356.6187253 -541.3677506 -2.9773147 555.1089094 361.8594615
## [1551] -156.7906066 -561.3514193 -529.0671205 -684.0202869 -311.3767917
## [1556] -282.2763143 666.8936309 981.3429941 163.1471676 -242.0540470
## [1561] -393.0072433 68.0627567 33.9008729 -837.2494376 688.9133752
## [1566] 1185.2844619 -153.0505268 -538.8485518 -252.4711894 -692.1905360
## [1571] -240.2724995 -270.1509013 657.7673362 173.7200028 -294.8902346
## [1576] -468.0331205 230.6063316 -161.0826090 -322.6724173 365.4214732
## [1581] 21.7728430 -645.0593720 258.4381465 193.3353976 -120.8603899
## [1586] 884.1133727 -345.1020794 945.7296533 451.8091693 -532.0363467
## [1591] -215.0660636 136.8797355 -596.6610134 -687.7398353 -484.7143832
## [1596] -64.9531686 91.0873769 -316.9195820 -343.7177556 -461.5558195
## [1601] -245.5614974 -268.0170839 102.2926604 138.8762951 -533.1365360
## [1606] 1316.6171261 277.7571261 -1010.2326340 229.7926902 -336.9654193
## [1611] -615.4206298 -52.5157755 -237.5480154 -365.3760819 -262.9761225
## [1616] -605.9091454 148.2815919 331.2981813 -233.9405584 197.8609576
## [1621] 336.2655811 -302.7208780 381.3827359 103.3206330 -23.8432616
## [1626] -576.7468623 -527.8658303 -491.2574650 -218.9896501 355.2569252
## [1631] -526.5304380 -376.7723301 -299.0235447 788.3041722 -783.1729561
## [1636] -373.6257871 212.1452083 -424.5300403 503.6110439 184.3641166
## [1641] 470.5864819 -174.5668515 160.7065886 98.1592798 -115.1938966
## [1646] 35.2460536 87.2512931 -391.1530605 -226.9350124 17.5623732
## [1651] 291.0348664 -146.5583549 220.6812707 334.0285127 489.9150333
## [1656] 395.8713919 106.9544720 487.8494309 721.3831296 305.8279838
## [1661] 172.7926571 295.6284770 446.5030224 315.1378834 151.4350432
## [1666] 327.8223400 822.2969403 770.2780229 1151.5571437 560.4421482
## [1671] 946.1113172 806.3252416 907.0857871 826.8964014 381.9663010
## [1676] -2363.3104686 -2430.2910805 -2338.5493138 -2311.5746214 -2245.1922262
## [1681] -2714.7634524 -2013.0233154 -2285.5496832 -2501.3378750 -2014.8037746
## [1686] -2441.8720643 -2287.8391237 -2282.4476716 -2293.5818634 -2010.6227991
## [1691] -2248.1234682 -2418.2587766 -2584.8465143 -2452.3613246 -2253.7413678
## [1696] -2635.5995413 -2493.1530390 -2148.2520070 -2780.8307924 -2443.6445849
## [1701] -2207.7881739 -447.0011693 142.2531229 -231.8365575 113.7479905
## [1706] 583.1296526 610.7232989 -76.8778377 136.7783383 288.1137904
## [1711] -421.1087484 311.4958086 380.9512607 -113.4070540 566.0004529
## [1716] 336.0074276 337.8071992 528.5825442 367.6848663 223.8189967
## [1721] 185.3828871 502.6171976 629.3956019 -0.4617547 130.8386563
## [1726] 345.7377497 411.7559257 961.9514873 337.8726994 564.4902910
## [1731] 620.9527866 209.9473412 663.2267434 394.5223690 1141.6989759
## [1736] 181.7598460 336.2010606 96.1930697 449.2136201 324.8117364
## [1741] 265.9711154 315.5586131 400.0877090 114.4128323 359.9774417
## [1746] 136.7981590 65.1526795 293.8925060 202.2204487 -4.6449643
## [1751] 276.9210033 522.2540286 181.0365126 137.3386314 209.9665126
## [1756] -36.2658369 317.5510672 412.9675969 519.3931860 371.3100079
## [1761] 357.3400079 507.4788572 501.8217248 458.2561332 213.2832980
## [1766] 979.9726770 334.9099647 60.2362910 435.1961631 362.9443524
## [1771] -81.5784487 323.6782362 63.4745923 531.5162179 -362.8363325
## [1776] 384.2975878 128.0892931 405.9864163 419.9243524 454.7450830
## [1781] 256.0091013 121.8491768 675.9358435 106.5148688 12.0128414
## [1786] 267.0218485 519.6665151 -195.4134616 141.8970431 358.6742602
## [1791] -176.4157398 194.7889244 -92.6901690 590.1318908 752.7572606
## [1796] 500.2497471 98.2719347 310.5843914 1018.8610306 647.0357272
## [1801] 1080.4631153 878.0584345 1038.9744711 925.2799115 967.7830348
## [1806] 796.9804437 1253.2338799 1248.8264802 1156.7768845 992.0259688
## [1811] 1288.2767152 1386.6658177 1205.7503930 962.7190738 929.2646786
## [1816] 769.2268978 1216.4995412 757.9039547 608.4827401 928.7185599
## [1821] 1390.3123175 644.0924063 1249.4742195 1003.9414889 882.1852033
## [1826] 286.9863748 1044.9239912 334.8216483 -561.4433654 -127.3880984
## [1831] 114.5016251 906.2141457 -104.1371511 -53.7951810 526.5592299
## [1836] -91.8330557 -564.4173795 -637.9615281 149.1544421 -256.3734733
## [1841] -343.0058934 -211.3798776 1069.9217920 -381.4790183 -107.3450822
## [1846] -684.2863267 162.4766230 709.2311685 335.6176824 991.1810132
## [1851] -129.4425733 -89.5247012 941.2128646 416.1724836 -164.4979158
## [1856] -153.4777174 -368.9902719 348.0242420 -32.7553313 -468.8374633
## [1861] 76.8147119 -195.3397472 208.4084520 -345.5514019 -520.0222238
## [1866] -189.8932632 46.4782627 -77.6852533 -309.2993604 225.7017081
## [1871] -300.4507510 -164.1428971 300.2689501 935.2895437 -344.0317556
## [1876] 53.4235138 -546.2506937 -387.3222578 770.1587401 426.6282195
## [1881] 210.6712764 -984.7331935 -197.4895704 -322.7264837 565.7853337
## [1886] 315.4718634 -411.3331802 312.2896326 -102.7591096 154.5223125
## [1891] 18.5882420 -820.3528631 10.7118700 -535.3729951 -155.2761159
## [1896] 185.7233677 253.6864321 -243.6742139 -695.1703600 -483.5787826
## [1901] 1267.3040186 1038.2479206 528.5533021 -29.9759764 -281.0326730
## [1906] -436.6571338 70.8562129 -191.5849993 773.1979231 -390.2778394
## [1911] -356.6187253 -541.3677506 -2.9773147 555.1089094 361.8594615
## [1916] -156.7906066 -561.3514193 -529.0671205 -684.0202869 -311.3767917
## [1921] -282.2763143 666.8936309 981.3429941 163.1471676 -242.0540470
## [1926] -393.0072433 68.0627567 33.9008729 -837.2494376 688.9133752
## [1931] 1185.2844619 -153.0505268 -538.8485518 -252.4711894 -692.1905360
## [1936] -240.2724995 -270.1509013 657.7673362 173.7200028 -294.8902346
## [1941] -468.0331205 230.6063316 -161.0826090 -322.6724173 365.4214732
## [1946] 21.7728430 -645.0593720 258.4381465 193.3353976 -120.8603899
## [1951] 884.1133727 -345.1020794 945.7296533 451.8091693 -532.0363467
## [1956] -215.0660636 136.8797355 -596.6610134 -687.7398353 -484.7143832
## [1961] -64.9531686 91.0873769 -316.9195820 -343.7177556 -461.5558195
## [1966] -245.5614974 -268.0170839 102.2926604 138.8762951 -533.1365360
## [1971] 1316.6171261 277.7571261 -1010.2326340 229.7926902 -336.9654193
## [1976] -615.4206298 -52.5157755 -237.5480154 -365.3760819 -262.9761225
## [1981] -605.9091454 148.2815919 331.2981813 -233.9405584 197.8609576
## [1986] 336.2655811 -302.7208780 381.3827359 103.3206330 -23.8432616
## [1991] -576.7468623 -527.8658303 -491.2574650 -218.9896501 355.2569252
## [1996] -526.5304380 -376.7723301 -299.0235447 788.3041722 -783.1729561
## [2001] -373.6257871 212.1452083 -424.5300403 503.6110439 184.3641166
## [2006] 470.5864819 -174.5668515 160.7065886 98.1592798 -115.1938966
## [2011] 35.2460536 87.2512931 -391.1530605 -226.9350124 17.5623732
## [2016] 291.0348664 -146.5583549 220.6812707 334.0285127 489.9150333
## [2021] 395.8713919 106.9544720 487.8494309 721.3831296 305.8279838
## [2026] 172.7926571 295.6284770 446.5030224 315.1378834 151.4350432
## [2031] 327.8223400 822.2969403 770.2780229 1151.5571437 560.4421482
## [2036] 946.1113172 806.3252416 907.0857871 826.8964014 381.9663010
## [2041] -2363.3104686 -2430.2910805 -2338.5493138 -2311.5746214 -2245.1922262
## [2046] -2714.7634524 -2013.0233154 -2285.5496832 -2501.3378750 -2014.8037746
## [2051] -2441.8720643 -2287.8391237 -2282.4476716 -2293.5818634 -2010.6227991
## [2056] -2248.1234682 -2418.2587766 -2584.8465143 -2452.3613246 -2253.7413678
## [2061] -2635.5995413 -2493.1530390 -2148.2520070 -2780.8307924 -2443.6445849
## [2066] -2207.7881739 -447.0011693 142.2531229 -231.8365575 113.7479905
## [2071] 583.1296526 610.7232989 -76.8778377 136.7783383 288.1137904
## [2076] -421.1087484 311.4958086 380.9512607 -113.4070540 566.0004529
## [2081] 336.0074276 337.8071992 528.5825442 367.6848663 223.8189967
## [2086] 185.3828871 502.6171976 629.3956019 -0.4617547 130.8386563
## [2091] 345.7377497 411.7559257 961.9514873 337.8726994 564.4902910
## [2096] 620.9527866 209.9473412 663.2267434 394.5223690 1141.6989759
## [2101] 181.7598460 336.2010606 96.1930697 449.2136201 324.8117364
## [2106] 265.9711154 315.5586131 400.0877090 114.4128323 359.9774417
## [2111] 136.7981590 65.1526795 293.8925060 202.2204487 -4.6449643
## [2116] 276.9210033 522.2540286 181.0365126 137.3386314 209.9665126
## [2121] -36.2658369 317.5510672 412.9675969 519.3931860 371.3100079
## [2126] 357.3400079 507.4788572 501.8217248 458.2561332 213.2832980
## [2131] 979.9726770 334.9099647 60.2362910 435.1961631 362.9443524
## [2136] -81.5784487 323.6782362 63.4745923 531.5162179 -362.8363325
## [2141] 384.2975878 128.0892931 405.9864163 419.9243524 454.7450830
## [2146] 256.0091013 121.8491768 675.9358435 106.5148688 12.0128414
## [2151] 267.0218485 519.6665151 -195.4134616 141.8970431 358.6742602
## [2156] -176.4157398 194.7889244 -92.6901690 590.1318908 752.7572606
## [2161] 500.2497471 98.2719347 310.5843914 1018.8610306 647.0357272
## [2166] 1080.4631153 878.0584345 1038.9744711 925.2799115 967.7830348
## [2171] 796.9804437 1253.2338799 1248.8264802 1156.7768845 992.0259688
## [2176] 1288.2767152 1386.6658177 1205.7503930 962.7190738 929.2646786
## [2181] 769.2268978 1216.4995412 757.9039547 608.4827401 928.7185599
## [2186] 1390.3123175 644.0924063 1249.4742195 1003.9414889 882.1852033
##
## $trend
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##
## $figure
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## [6] 114.5016251 906.2141457 -104.1371511 -53.7951810 526.5592299
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## [356] 769.2268978 1216.4995412 757.9039547 608.4827401 928.7185599
## [361] 1390.3123175 644.0924063 1249.4742195 1003.9414889 882.1852033
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"
plot(dpd_ts)
library(zoo)
rollmean(dpd_ts, 3)
## Time Series:
## Start = c(1, 2)
## End = c(2, 364)
## Frequency = 365
## date ca nb_ventes
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## 2.942466 19396 16560.263 891.6667
## 2.945205 19397 15296.042 833.3333
## 2.947945 19398 15708.852 905.3333
## 2.950685 19399 16207.822 912.0000
## 2.953425 19400 16382.583 941.0000
## 2.956164 19401 16400.473 907.3333
## 2.958904 19402 15780.093 909.0000
## 2.961644 19403 16065.959 921.3333
## 2.964384 19404 15758.651 908.0000
## 2.967123 19405 16903.237 938.3333
## 2.969863 19406 17003.425 936.0000
## 2.972603 19407 17081.747 959.0000
## 2.975342 19408 16680.582 925.6667
## 2.978082 19409 16580.326 938.3333
## 2.980822 19410 16326.682 922.6667
## 2.983562 19411 15418.653 905.0000
## 2.986301 19412 15403.727 899.6667
## 2.989041 19413 15757.953 896.3333
## 2.991781 19414 17078.927 968.3333
## 2.994521 19415 17860.227 987.0000
plot(rollmean(dpd_ts, 3))
Mise à part l’impact qu’ont eu les données manquantes du mois
d’octobre 2021 sur nos moyennes mobiles (chiffre d’affaires et nombre de
ventes), nous pouvons clairement voir que ni l’une ni l’autre ne
semblent connaitre de phénomène de saisonnalité. De plus, ces moyennes
mobiles nous démontrent parfaitement la relative stabilité du CA au
cours du temps.
categ_genre <- table(data$categ, data$sex)
categ_genre
##
## f m
## 0 206220 209460
## 1 114899 112270
## 2 17283 19200
Nous pouvons déjà constater qu’il y a pratiquement autant de ventes chez les hommes que chez les femmes dans chaque catégorie
library(questionr)
lprop(categ_genre)
##
## f m Total
## 0 49.6 50.4 100.0
## 1 50.6 49.4 100.0
## 2 47.4 52.6 100.0
## All 49.8 50.2 100.0
Effectuons un test de Khi-Deux afin de vérifier quelle hypothèse nous allons accepter : Admettons en tant qu’hypothèse nulle (H0) que la catégorie des livres achetés est liée au genre du client. Admettons en tant qu’hypothèse alternative (H1) que la catégorie des livres achetés n’est pas liée au genre du client.
library(stats)
chisq.test(categ_genre)
##
## Pearson's Chi-squared test
##
## data: categ_genre
## X-squared = 147, df = 2, p-value < 2.2e-16
La p-value étant nettement inférieure à 5% ou 0.05, nous pouvons rejeter H0 et admettre que la catégorie des livres achetés n’est pas liée au genre du client.
library(questionr)
chisq.residuals(categ_genre)
##
## f m
## 0 -1.86 1.85
## 1 5.16 -5.14
## 2 -6.61 6.58
Représentons graphiquement ces résultats afin de mieux les appréhender :
library(graphics)
mosaicplot(categ_genre, las = 3, shade = TRUE)
Il n’y a pas de lien établi entre le genre du client et la catégorie
des livres achetés.
data_f <- data[(data$sex == "f"),]
data_m <- data[(data$sex == "m"),]
head(data_f)
## client_id id_prod date session_id price categ sex birth age
## 106 c_1000 1_480 2023-01-06 s_322978 19.08 1 f 1966 57
## 107 c_1000 1_267 2021-12-01 s_127695 27.99 1 f 1966 57
## 108 c_1000 1_719 2022-08-11 s_251709 41.99 1 f 1966 57
## 109 c_1000 1_378 2022-02-14 s_164815 26.61 1 f 1966 57
## 110 c_1000 1_325 2021-05-31 s_42154 27.99 1 f 1966 57
## 111 c_1000 1_441 2022-01-30 s_157167 24.99 1 f 1966 57
## annee_mois jour mois annee
## 106 2023-01-01 6 1 2023
## 107 2021-12-01 1 12 2021
## 108 2022-08-01 11 8 2022
## 109 2022-02-01 14 2 2022
## 110 2021-05-01 31 5 2021
## 111 2022-01-01 30 1 2022
head(data_m)
## client_id id_prod date session_id price categ sex birth age annee_mois
## 1 c_1 0_1378 2021-08-23 s_79696 13.96 0 m 1955 68 2021-08-01
## 2 c_1 0_1090 2021-12-19 s_136532 13.78 0 m 1955 68 2021-12-01
## 3 c_1 0_1547 2021-09-08 s_86739 8.99 0 m 1955 68 2021-09-01
## 4 c_1 1_713 2021-11-15 s_120172 33.99 1 m 1955 68 2021-11-01
## 5 c_1 1_364 2022-06-15 s_224447 10.30 1 m 1955 68 2022-06-01
## 6 c_1 0_2277 2021-09-06 s_85977 10.99 0 m 1955 68 2021-09-01
## jour mois annee
## 1 23 8 2021
## 2 19 12 2021
## 3 8 9 2021
## 4 15 11 2021
## 5 15 6 2022
## 6 6 9 2021
library(dplyr)
library(magrittr)
data_m_categ <- data_m %>% group_by(categ) %>% summarise(nb_achats = n(), prop = round(nb_achats/340930*100, digits = 2))
data_f_categ <- data_f %>% group_by(categ) %>% summarise(nb_achats = n(), prop = round(nb_achats/338402*100 , digits = 2))
library(magrittr)
library(ggplot2)
library(hrbrthemes)
library(graphics)
par(mfrow=c(2,1))
data_m_categ %>%
ggplot(aes(x="", y=prop, fill=categ)) +
geom_bar(stat="identity", width=1, color="white") +
coord_polar("y", start=0) +
theme_void() +
ggtitle("Proportion des ventes chez les hommes, par catégorie")
data_f_categ %>%
ggplot(aes(x="", y=prop, fill=categ)) +
geom_bar(stat="identity", width=1, color="white") +
coord_polar("y", start=0) +
theme_void() +
ggtitle("Proportion des ventes chez les femmes, par catégorie")
Il ne semble pas y avoir de lien établi entre le genre du client et les catégories des livres achetés.
Étant donné la taille de notre échantillon et d’après la loi des grands nombres, nous pouvons supposer que la moyenne empirique tend vers l’espérance et donc vers une loi normale. Nous pouvons donc effectuer un test d’anova (analyse des variances) afin de vérifier quelle hypothèse nous allons accepter : L’hypothèse nulle (H0) dit que les moyennes de tous les groupes sont égales (le montant total des achats n’est pas lié à l’âge du client). L’hypothèse alternative (H1) dit que la moyenne d’au moins l’un des groupes est différente de celles des autres (le montant total des achats est lié à l’âge du client).
library(onewaytests)
##
## Attaching package: 'onewaytests'
## The following object is masked from 'package:questionr':
##
## describe
aov.test(ca~factor(age), ca_per_client)
##
## One-Way Analysis of Variance (alpha = 0.05)
## -------------------------------------------------------------
## data : ca and factor(age)
##
## statistic : 0.900226
## num df : 75
## denom df : 8524
## p.value : 0.7176108
##
## Result : Difference is not statistically significant.
## -------------------------------------------------------------
La p-value étant largement supérieure à 5% ou 0.05, nous pouvons accepter H0 et admettre que le montant total des achats n’est pas lié à l’âge du client.
Pour vérification, utilisons la corrélation des rangs de Spearman (moins sensible aux valeurs extrêmes) :
library(stats)
cor(ca_per_client$age, ca_per_client$ca, method = "spearman")
## [1] -0.1849352
Nous avons bien la confirmation qu’il n’existe pas de lien entre âge et motant total des achats dans ce cas précis (la corrélation est plus proche de 0 que de 1 ou -1).
library(dplyr)
library(magrittr)
library(ggplot2)
library(graphics)
ca_per_client %>%
group_by(age) %>%
summarise(ca=mean(ca)) %>%
ggplot(aes(x=age, y=ca)) +
geom_bar(stat = "identity", width=0.5, color="grey", fill="lightblue") +
xlab("Âge") +
ylab("Montant total des achats") +
ggtitle("Montant total des achats réalisé en fonction de l'âge (moyenne)") +
theme_ipsum()
L’âge ne semble effectivement pas influencer le montant total des achats. En effet, bien que le montant total des achats des clients appartenant à la classe d’âge des actifs soit légèrement supérieur à celui des clients plus âgés, cette différence n’est pas suffisamment significative et nous pouvons clairement observer que les montants sont relativement bien équilibrés le long de l’axe des abscisses.
Effectuons de nouveau un test d’analyse des variances afin de vérifier laquelle des 2 hypothèses nous allons accepter : L’hypothèse nulle (H0) dit que les moyennes de tous les groupes sont égales (la taille du panier moyen n’est pas liée à l’âge du client). L’hypothèse alternative (H1) dit que la moyenne d’au moins l’un des groupes est différente de celles des autres (la taille du panier moyen est liée à l’âge du client).
library(onewaytests)
aov.test(panier_moyen~factor(age), ca_per_client)
##
## One-Way Analysis of Variance (alpha = 0.05)
## -------------------------------------------------------------
## data : panier_moyen and factor(age)
##
## statistic : 198.3447
## num df : 75
## denom df : 8524
## p.value : 0
##
## Result : Difference is statistically significant.
## -------------------------------------------------------------
La p-value étant nettement inférieure à 5% ou 0.05, nous pouvons rejeter H0 et admettre que la taille du panier moyen est liée à l’âge du client.
Pour vérification :
library(stats)
cor(ca_per_client$age, ca_per_client$panier_moyen)
## [1] -0.5131829
Cette fois, le coefficient de corrélation de Pearson nous indique la présence d’une faible corrélation linéaire négative (plus l’âge augmente, plus le montant du panier moyen diminue).
library(dplyr)
library(magrittr)
library(ggplot2)
library(graphics)
ca_per_client %>%
group_by(age) %>%
summarise(panier_moyen=mean(panier_moyen)) %>%
ggplot(aes(x=age, y=panier_moyen)) +
geom_bar(stat = "identity", width=0.5, color="grey", fill="lightblue") +
xlab("Âge") +
ylab("Montant du panier moyen") +
ggtitle("Taille du panier moyen en fonction de l'âge (moyenne)") +
theme_ipsum()
Le montant du panier moyen des clients les plus jeunes (jusqu’à
environ 32 ans) est beaucoup plus élevé que celui des autres clients. Il
représente plus du double de celui des autres clients.
library(dplyr)
library(magrittr)
library(vctrs)
##
## Attaching package: 'vctrs'
## The following object is masked from 'package:dplyr':
##
## data_frame
frequence_mensuelle <- data %>% group_by(client_id, annee, mois) %>% summarise(nb_achats=vec_unique_count(session_id))
## `summarise()` has grouped output by 'client_id', 'annee'. You can override
## using the `.groups` argument.
frequence_mensuelle <- frequence_mensuelle %>% group_by(client_id) %>% summarise(freq_mensu_moyenne=nb_achats/342366)
## `summarise()` has grouped output by 'client_id'. You can override using the
## `.groups` argument.
frequence_mensuelle <- merge(frequence_mensuelle, clients2)
head(frequence_mensuelle)
## client_id freq_mensu_moyenne sex birth age
## 1 c_1 2.920851e-06 m 1955 68
## 2 c_1 1.168340e-05 m 1955 68
## 3 c_1 2.920851e-06 m 1955 68
## 4 c_1 5.841702e-06 m 1955 68
## 5 c_1 2.920851e-06 m 1955 68
## 6 c_1 5.841702e-06 m 1955 68
library(dplyr)
library(magrittr)
frequence_age <- frequence_mensuelle %>% group_by(age) %>% summarise(freq_mensuelle=round(sum(freq_mensu_moyenne), digits = 5))
head(frequence_age)
## # A tibble: 6 × 2
## age freq_mensuelle
## <dbl> <dbl>
## 1 19 0.0251
## 2 20 0.0075
## 3 21 0.00761
## 4 22 0.0071
## 5 23 0.00707
## 6 24 0.0195
Effectuons un test de correlation afin de vérifier laquelle des 2 hypothèses nous allons rejeter : Admettons en tant qu’hypothèse nulle (H0) que la fréquence des achats n’est pas liée à l’âge du client. Admettons en tant qu’hypothèse alternative (H1) que la fréquence des achats est liée à l’âge du client.
library(stats)
cor.test(frequence_age$age, frequence_age$freq_mensuelle, method=c("pearson", "kendall", "spearman"), alternative="two.sided", conf.level=0.95)
##
## Pearson's product-moment correlation
##
## data: frequence_age$age and frequence_age$freq_mensuelle
## t = -5.7072, df = 74, p-value = 2.238e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.6920393 -0.3740004
## sample estimates:
## cor
## -0.5528402
La p-value étant nettement inférieure à 5% ou 0.05, nous pouvons rejeter H0 et admettre que la fréquence des achats est liée à l’âge du client.
plot(frequence_age$age, frequence_age$freq_mensuelle, xlab="Âge", ylab="Fréquence des achats", main="Fréquence mensuelle d'achat par âge")
Au vu des des précédents graphiques, nous pouvons admettre qu’il existe effectivement une corrélation entre fréquence d’achat et âge. En effet nous avons pu constater que les clients les plus jeunes (les moins de 20 ans) et les clients les plus âgés (les plus de 60 ans) commandent moins et donc moins fréquemment que les clients appartenant aux catégories intermédiaires (entre 20 et 59 ans).
Effectuons un test de Kruskal-Wallis (test non paramétrique, n’induisant aucune loi et permettant de comparer 2 échantillons ou plus) afin de vérifier laquelle des 2 hypothèses nous allons rejeter : L’hypothèse nulle (H0) dit que les paramètres de la distribution sont les mêmes dans chaque groupe (la catégorie des livres achetés n’est pas liée à l’âge du client). L’hypothèse alternative (H1) dit que les paramètres de la distribution diffèrent dans au moins l’un des groupes (la catégorie des livres achetés est liée à l’âge du client dans au moins l’un des cas).
library(stats)
kruskal.test(data$age, data$categ)
##
## Kruskal-Wallis rank sum test
##
## data: data$age and data$categ
## Kruskal-Wallis chi-squared = 79351, df = 2, p-value < 2.2e-16
La p-value étant nettement inférieure à 5% ou 0.05, nous pouvons rejeter H0 et admettre que la catégorie des livres achetés est liée à l’âge du client.
library(ggplot2)
library(viridis)
## Loading required package: viridisLite
library(hrbrthemes)
data %>%
ggplot(aes(x=categ, y=age, fill=categ)) +
geom_boxplot() +
scale_fill_viridis(discrete = TRUE, alpha=0.6, option="A") +
theme_ipsum() +
theme(legend.position="none", plot.title = element_text(size=11)) +
ggtitle("Répartition de l'âge des clients en fonction des catégories achetées") +
xlab("")
categ <- rep(c("0" , "1" , "2"), 4)
tranche_age <- c(rep("Moins de 20 ans", 3), rep("20 à 39 ans", 3), rep("40 à 59 ans", 3), rep("60 ans et plus", 3))
nb_ventes <- c(3418, 5717, 6012, 131025, 60193, 27747, 239419, 107710, 1825, 41818, 53547, 899)
proportion_ventes <- c(22.56, 37.75, 39.69, 59.84, 27.49, 12.67, 68.61, 30.87, 0.52, 43.44, 55.63, 0.93)
data_categ_age <- data.frame(categ, tranche_age, nb_ventes, proportion_ventes)
library(dplyr)
library(magrittr)
library(ggplot2)
library(viridis)
data_categ_age %>%
ggplot(aes(fill=categ, y=proportion_ventes, x=tranche_age)) +
geom_bar(position="fill", stat="identity") +
scale_fill_viridis(discrete = T, option = "G") +
xlab("Tranche d'âge") +
ylab("Proportion des ventes") +
ggtitle("Répartition des ventes par tranche d'âge") +
theme_ipsum()
Les moins de 20 ans achètent majoritairement des livres
correspondant à la catégorie 2. Nous pouvons également constater que
plus l’âge augmente, moins la catégorie 2 est achetée.
library(dplyr)
library(magrittr)
library(ggplot2)
library(viridis)
data_categ_age %>%
ggplot(aes(fill=tranche_age, y=nb_ventes, x=categ)) +
geom_bar(position="fill", stat="identity") +
scale_fill_viridis(discrete = T) +
xlab("Catégories") +
ylab("Proportion des ventes") +
ggtitle("Répartition des ventes par catégorie") +
theme_ipsum()
Ce graphique nous montre, quant à lui, que les clients âgés de moins
de 40 ans sont les principaux consommateurs de la catégorie 2 avec près
de 90% des ventes réalisées (les adultes entre 20 et 39 ans
représentants à eux seuls environ 75% des acheteurs).
L’analyse des moyennes mobiles nous a permis d’affirmer que ni les ventes ni le chiffre d’affaires ne connaissent de phénomène de saisonnalité. Nous pouvons donc utiliser ARIMA afin de poursuivre notre analyse.
library(tsibble)
dpm2 <- dpm
dpm2$annee_mois <- yearmonth(dpm2$annee_mois)
Nous devons d’abord choisir les ordres p, d et q de notre modèle. Nous commençons par vérifier si la série doit être différenciée pour obtenir une série stationnaire. La fonction unitroot_ndiffs effectue un test statistique pour déterminer le nombre minimum de différenciations à réaliser.
library(feasts)
## Loading required package: fabletools
##
## Attaching package: 'fabletools'
## The following objects are masked from 'package:DescTools':
##
## MAE, MAPE, MSE, RMSE
library(fabletools)
unitroot_ndiffs(dpm2$ca)
## ndiffs
## 0
Ici, le résultat est 0 donc aucune différenciation n’est nécessaire (d=0).
library(feasts)
library(fabletools)
dpm_tsb <- as_tsibble(dpm2)
## Using `annee_mois` as index variable.
library(stats)
acf(dpm_tsb$ca, lag.max = 12, type = "correlation")
On voit que le CA d’un mois m n’influe pas sur le CA des mois suivants. Effectuons maintenant un test de stationarité (test de Dickey-Fuller) :
library(tseries)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
adf.test(dpm_tsb$ca)
##
## Augmented Dickey-Fuller Test
##
## data: dpm_tsb$ca
## Dickey-Fuller = -2.5404, Lag order = 2, p-value = 0.3665
## alternative hypothesis: stationary
L’hypothèse H0 est que la série comporte une racine unitaire (CA non stationnaire). L’hypothèse H1 est que la série ne comporte pas de racine unitaire (CA stationnaire). La p-value étant supérieure à 0,05, nous allons accepter H0 et admettre que le CA n’est pas stationnaire. Hors, la stationnarité étant une condition nécessaire pour représenter une série temporelle avec un modèle ARIMA, créons une série différenciée sur laquelle nous effectuerons un nouveau test de stationnarité.
library(tseries)
diff_ca <- dpm_tsb$ca[2:24]-dpm_tsb$ca[1:23]
adf.test(diff_ca)
##
## Augmented Dickey-Fuller Test
##
## data: diff_ca
## Dickey-Fuller = -3.5499, Lag order = 2, p-value = 0.05696
## alternative hypothesis: stationary
Au vue de la valeur de la p-value, nous prendrons le parti d’accepter l’hypothèse H1 disant que la série ne comporte pas de racine unitaire et que, par conséquent, le CA est stationnaire. Nous pouvons donc poursuivre en réalisant nos prévisions sur diff_ca. Réalisons un nouveau test d’auto-corrélation :
library(tseries)
acf(diff_ca, lag.max = 12, type = "correlation")
Sur diff_ca, nous pouvons observer un retard de 1. Voyons maintenant quel modèle ARIMA nous allons utiliser grâce à la fonction auto.arima qui va déterminer pour nous les valeurs de p, d et q :
library(forecast)
##
## Attaching package: 'forecast'
## The following object is masked from 'package:DescTools':
##
## BoxCox
auto.arima(diff_ca)
## Series: diff_ca
## ARIMA(0,0,1) with zero mean
##
## Coefficients:
## ma1
## -0.9527
## s.e. 0.2572
##
## sigma^2 = 1.846e+09: log likelihood = -278.63
## AIC=561.26 AICc=561.86 BIC=563.53
library(stats)
arima(diff_ca, order=c(0,0,1))
##
## Call:
## arima(x = diff_ca, order = c(0, 0, 1))
##
## Coefficients:
## ma1 intercept
## -0.9997 1194.649
## s.e. 0.1303 1189.847
##
## sigma^2 estimated as 1.628e+09: log likelihood = -278.14, aic = 562.28
library(stats)
residuals(arima(diff_ca, order=c(0,0,1)))
## Time Series:
## Start = 1
## End = 23
## Frequency = 1
## [1] -5281.096 9665.294 -1880.424 -3677.803 -4542.845 18195.565
## [7] -159844.967 42163.788 45796.321 39711.229 44973.161 20892.158
## [13] -3419.478 19004.275 -3931.693 9533.076 3586.114 -9784.770
## [19] 3020.221 -9265.319 3186.371 9048.911 -52095.550
library(stats)
predict(arima(diff_ca, order=c(0,0,1)), n.ahead = 3)
## $pred
## Time Series:
## Start = 24
## End = 26
## Frequency = 1
## [1] 52184.591 1194.649 1194.649
##
## $se
## Time Series:
## Start = 24
## End = 26
## Frequency = 1
## [1] 41171.49 57048.87 57048.87
library(forecast)
forecast(arima(diff_ca, order=c(0,0,1)), h=3)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 24 52184.591 -578.7982 104947.98 -28510.05 132879.2
## 25 1194.649 -71916.4149 74305.71 -110619.07 113008.4
## 26 1194.649 -71916.4149 74305.71 -110619.07 113008.4
autoplot(forecast(arima(diff_ca, order=c(0,0,1)), h=3))